3x*(x+1)=9

Solution for 3x*(x+1)=9 equation:

3x(x+1)=9

We move all terms to the left:

3x(x+1)-(9)=0

We multiply parentheses

3x^2+3x-9=0

a = 3; b = 3; c = -9;
Δ = b2-4ac
Δ = 32-4·3·(-9)
Δ = 117
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{117}=\sqrt{9*13}=\sqrt{9}*\sqrt{13}=3\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3\sqrt{13}}{2*3}=\frac{-3-3\sqrt{13}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3\sqrt{13}}{2*3}=\frac{-3+3\sqrt{13}}{6}
$